I really don't think this question can be answered in general as the circuмstances of public schools and of Novus Ordo schools differs throughout the world.  

In central Indiana (USA) I would say that the Novus Ordo schools are much better than the public schools through the eighth grade.  Once a student graduates to high school, however, there is really not much difference.  

The lower grades in the Novus Ordo schools don't teach religion very well, but one almost never hears of outright hostility toward the Church while discipline and academic standards are maintained quite well.  Obviously, the public schools don't teach religion at all and, depending upon where one attends school, the discipline and academic standards may or may not be well maintained depending upon which school one attends, though there is not generally a problem in the lower grades.

At the high school level, however, one begins to hear of hostility against the Church by faculty and the newspapers seem to report on some sort of scandal in schools, both public and Novus Ordo every few months.  Based on my actual meetings with students and graduates of the archdiocesan high schools, I would say that it would probably be better for the students' souls to NOT attend these schools as any knowledge they once had of the Church seems to disappear and they are positively hostile to the Church.

Whether or not this is universal, though, I simply don't know.

I do have a question of your post:  The way you wrote it you seem to connect, at least somewhat, the fact that there was a Hitler fan in your school and your impression that there is "a bit of Tradition" in your town.  While I do believe that some of the history of Hitler has been exaggerated, he was anti-Catholic to the core.  Tradition is not a fan of Hitler in any way.  In fact, the pope wrote an encyclical, Mit Brennender Sorge, against what Hitler was doing, and its official publication is in the German language (rather than Latin) making an absolutely direct point that this encyclical is specifically for the German-speaking peoples of the day.